IEEE INFOCOM 2007 Anchorage Distributed Placement of Service

IEEE INFOCOM 2007 – Anchorage Distributed Placement of Service Facilities in Large-Scale Networks *Nikolaos Laoutaris nlaout@eecs. harvard. edu Postdoc Fellow Harvard University Joint work with: Georgios Smaragdakis†, Konstantinos Oikonomou‡, Ioannis Stavrakakis§, Azer Bestavros† §U. Athens, ‡Ionian U. , †Boston U. * Sponsored under a Marie Curie Outgoing International Fellowship of the EU at Boston University and the University of Athens

Where to install the service facility? n n Distribution of software updates and patches (e. g. , Windows Update) Real time distribution of virus definition files Fixed deployment Dynamic deployment n n time-of-day effects flash crowds Being able to adjust the number and the location of service facilities dynamically should be more economic than fixed over-provisioning… 2

A setting for dynamic service deployment Generic Service Host Service Facility Flash Crowd 3

Let’s abstract the problem n n We have: n a network (let’s think AS-level granularity) n a demand (# downloads from each AS) We want: n n n a request [the number of service facilities] their location a server (software) Theory has the solution n n Uncapacitated k-median Uncapacitated facility location a really nice read 4

UKM and UFL n Uncapacited K-median (UKM): Given a set of points V with pair-wise distance function d and service demands s(vj), ∀ vj ∈V, select up to k points to act as medians (facilities) so as to minimize the service cost C(V, s, k): where m(vj) is the median that is closer to vj. n Uncapacited Facility Location (UFL): Given a set of points V with pair-wise distance function d, service demands s(vj), ∀ vj ∈V, and facility costs f(vj), ∀vj∈V, select a subset of points F to act as facilities so as to minimize: 5

Centralized UKM and UFL: Not very practical for Internet-scale applications n Limitations: n n We need distributed versions: n n need entire topology and demand information in one place one BIG computation no way for incremental re-optimization using limited local topology/demand info employing multiple small computations keeping changes local Previous work: n Moscibroda & Wattenhofer (PODC’ 05) 6

Common framework for distributed UKM and UFL n Initialization: select an initial set of nodes to be the facilities n Iterative improvement: select an existing facility and “process” it using local information only n n change its location (in the case of UKM) change its location and/or merge it with other facilities or spawn additional copies of it (in the case of UFL) continue with the next facility in round-robin manner Stopping condition: when “processing” yields no improvement for any facility 7

Processing a facility “ring” nodes r-ball (r=2) r-ball (r=1) n const # facilities 1 -median in r-ball n var # facilities UFL in r-ball n but there is a PROBLEM n nodes outside the r-ball … are totally neglected and a SOLUTION to it n map ring demand on the “skin” of the r-ball 8

Intersecting r-balls merge into r-shapes n r-ball r-shape r-ball n when 2 or more r-balls intersect we merge them if J facilities in the rshape n n J-median (const facilities) UFL (var facilities) r-shape provides for a way to reduce the # facilities if needed we put a restriction on the max-size of r-shapes 9

Selecting the radius r Small radius: + limited local information for the r -balls (scalability) − performance penalty (easier to run into bad local minima) Since most networks are smallworlds we keep r small (1≤r≤ 3) 10

Case Study: The AS-level Topology n 497 peer AS’s in the core of the Internet (Subramanian et al. ’ 02) load s(vj)= # AS’s with costumer-provider relationship to vj distance d(vi, vj)= # intermediate AS’s from vi vj n centralized vs distributed n n n UKM vs d. UKM(r) UFL vs d. UFL(r) social cost and # iterations 11

Placing k servers on the AS-level map 1% 3% #facilities: % of nodes 5% 1% 3% 5% #facilities: % of nodes 12

Selecting the right number of servers aka d. UFL(r) n Need a model for f(vj), the cost of placing a server at GSH vj n Uniform: all GSH’s charge the same n Degree-based: proportional to the degree of vj 13

Wrap up n Placement of service facility can be casted as a discrete location problem n Existing centralized solutions are not practical n Instead multiple local re-optimizations n n n exact info for a limited neighborhood of radius r approximate info for the surrounding “ring” Good approximation (experimental) even for very small radius 14

Thank you Q ?